Gravitational radiation from cosmic (super)strings: bursts, stochastic background, and observational windows

TL;DR

This paper reexamines gravitational-wave signals from cosmic strings, including cosmic superstrings, by introducing two key extensions to the standard network: a reduced reconnection probability $p$ and a variable loop-size parameter $\epsilon$. It analyzes both GW bursts from cusps and the stochastic GW background, deriving how the observables depend on $p$ and $\epsilon$ and showing that previous results are largely robust except in extreme small-$\epsilon$ regimes. The study highlights that lower $p$ generally enhances detectability in both bursts and the stochastic background, while very small $\epsilon$ can suppress signals in certain frequency bands, especially for small $G\mu$. It also connects these theoretical insights to current and future pulsar timing array sensitivities, arguing for renewed pulsar data analyses and improved string-network simulations to constrain $\alpha$ and the cusp rate $c$ for precise predictions.

Abstract

The gravitational wave (GW) signals emitted by a network of cosmic strings are reexamined in view of the possible formation of a network of cosmic superstrings at the end of brane inflation. The reconnection probability $p$ of intersecting fundamental or Dirichlet strings might be much smaller than 1, and the properties of the resulting string network may differ significantly from those of ordinary strings (which have $p=1$). In addition, it has been recently suggested that the typical length of newly formed loops may differ by a factor $ε\ll 1$ from its standard estimate. Here, we analyze the effects of the two parameters $p$ and $ε$ on the GW signatures of strings. We consider both the GW bursts emitted from cusps of oscillating string loops, which have been suggested as candidate sources for the LIGO/VIRGO and LISA interferometers, and the stochastic GW background, which may be detectable by pulsar timing observations. In both cases we find that previously obtained results are \textit{quite robust}, at least when the loop sizes are not suppressed by many orders of magnitude relative to the standard scenario. We urge pulsar observers to reanalyze a recently obtained 17-year combined data set to see whether the large scatter exhibited by a fraction of the data might be due to a transient GW burst activity of some sort, e.g. to a near cusp event.

Figures (6)

• Figure 1: Effect of a reconnection probability $10^{-3} \leq p \leq 1$ on the gravitational wave amplitude of bursts emitted by cosmic string cusps in the LIGO/VIRGO frequency band ($f_{ligo} =150$ Hz), as a function of the string tension parameter $G \, \mu$ (in a base-$10$ log-log plot). Here, as in the following figures, the average number of cusps per loop oscillation is assumed to be $c=1$. The horizontal dashed lines indicate the one sigma noise levels (after optimal filtering) of LIGO 1 (initial detector) and LIGO 2 (advanced configuration).
• Figure 2: Effect of a reconnection probability $10^{-3} \leq p \leq 1$ on the gravitational wave amplitude of bursts emitted by cosmic string cusps in the LISA frequency band ($f_{lisa} =3.88 \times 10^{-3}$ Hz) , as a function of the string tension parameter $G \, \mu$ (in a base-$10$ log-log plot). The horizontal dashed line indicates the one sigma noise level (after optimal filtering) of the LISA detector.
• Figure 3: Effect of a smaller fractional loop-length parameter $10^{-12} \leq \epsilon \equiv \alpha/(50 G \mu) \leq 1$ on the gravitational wave amplitude of bursts emitted by cosmic string cusps in the LIGO/VIRGO frequency band ($f_{ligo} =150$ Hz), as a function of the string tension parameter $G \, \mu$ (in a base-$10$ log-log plot). The horizontal dashed lines indicate the one sigma noise levels (after optimal filtering) of LIGO 1 (initial detector) and LIGO 2 (advanced configuration).
• Figure 4: Effect of a smaller fractional loop-length parameter $10^{-12} \leq \epsilon \equiv \alpha/(50 G \mu) \leq 1$ on the gravitational wave amplitude of bursts emitted by cosmic string cusps in the LISA frequency band ($f_{lisa} =3.88 \times 10^{-3}$ Hz) , as a function of the string tension parameter $G \, \mu$ (in a base-$10$ log-log plot). The horizontal dashed line indicates the one sigma noise level (after optimal filtering) of the LISA detector.
• Figure 5: Effect of a reconnection probability $10^{-3} \leq p \leq 1$ on the fractional contribution $\Omega_g(f_{psr})$ (around the frequency $f_{psr} \sim 1/(10 {\rm yr})$) to the cosmological closure density of the stochastic GW noise due to overlapping GW bursts emitted by a network of strings. [Base-$10$ log-log plot.] The upper (solid) horizontal line indicates the upper limit $\Omega_g < 6 h^{-2}\times 10^{-8}$ derived from 8 years of high-precision timing of two millisecond pulsars: PSR 1855+09 and PSR 1937+21. The middle (dashed) horizontal line indicates the potential sensitivity of 17 years of high-precision timing of PSR 1855+09 (see text). The lower (dashed) horizontal line indicates the expected sensitivity from the timing of the set of pulsars to be hopefully detected by a square-kilometer-array of radio telescopes.